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Serga [27]
2 years ago
9

In a sample of 41 temperature readings taken from the freezer of a restaurant, the mean is 29.7 degrees and the population stand

ard deviation is 2.7 degrees. What would be the 80% confidence interval for the temperatures in the freezer?
Mathematics
1 answer:
yKpoI14uk [10]2 years ago
7 0

Answer: =(29.1596\text{ degrees},\ 30.2404\text{ degrees})

Step-by-step explanation:

Given: Sample size: n = 41

Sample mean \overline{x}= 29.7 degrees

Population standard deviation \sigma=2.7 degrees

Confidence level (c) =  80% =0.80

Significance level (a) = 1- c = 1-0.80 = 0.20

z-score for 80% confidence level : z = 1.2816   [from z-table]

Confidence level for population mean :-

\overline{x}\pm z\dfrac{\sigma}{\sqrt{n}}

=29.7\pm ( 1.2816)\dfrac{2.7}{\sqrt{41}}

=29.7\pm ( 1.2816)\dfrac{2.7}{6.403124}

=29.7\pm ( 1.2816)(0.42167)

=29.7\pm 0.5404

=(29.7-0.5404,\ 29.7+0.5404)

=(29.1596,\ 30.2404)

Hence, 80% confidence interval for the temperatures in the freezer =(29.1596\text{ degrees},\ 30.2404\text{ degrees})

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